Question 1200420: 29% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
Found 2 solutions by ElectricPavlov, ikleyn:
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! **a) Probability of exactly three adults favoring the use of drones**
* This is a binomial probability problem.
* **Formula:**
P(X = k) = (nCk) * p^k * (1-p)^(n-k)
where:
* n = number of trials (12 adults)
* k = number of successes (3 adults favoring drone use)
* p = probability of success (0.29)
* (1-p) = probability of failure (0.71)
* nCk = binomial coefficient (number of combinations of n items taken k at a time)
* **Calculation:**
P(X = 3) = (12C3) * (0.29)^3 * (0.71)^(12-3)
P(X = 3) = 220 * 0.024389 * 0.040354
P(X = 3) ≈ 0.2173
* **Probability of exactly three adults favoring the use of drones is approximately 0.2173 or 21.73%.**
**b) Probability of at least four adults favoring the use of drones**
* P(X ≥ 4) = P(X = 4) + P(X = 5) + ... + P(X = 12)
* This can be calculated using the binomial probability formula for each value of X from 4 to 12 and summing the probabilities.
* **Alternatively, we can use the complement:**
P(X ≥ 4) = 1 - P(X < 4)
P(X ≥ 4) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)]
* Calculate each of these probabilities using the binomial formula as in part (a).
* **Using a calculator or statistical software:**
P(X ≥ 4) ≈ 0.3205
* **Probability of at least four adults favoring the use of drones is approximately 0.3205 or 32.05%.**
**c) Probability of less than eight adults favoring the use of drones**
* P(X < 8) = P(X = 0) + P(X = 1) + ... + P(X = 7)
* Calculate each of these probabilities using the binomial formula as in part (a).
* **Using a calculator or statistical software:**
P(X < 8) ≈ 0.9589
* **Probability of less than eight adults favoring the use of drones is approximately 0.9589 or 95.89%.**
**Note:** These calculations can be performed using statistical software like R, Python (with libraries like SciPy or NumPy), or online calculators.
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
29% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected.
Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is
(a) exactly three, (b) at least four, (c) less than eight.
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In the post by @ElectricPavlov, all calculations, all numbers, and all answers are INCORRECT.
The correct answers are:
(a) 0.246. (b) 0.4765. (c) 0.9924.
I checked using the online Binomial distribution calculator
https://stattrek.com/online-calculator/binomial
which is proven to be 100% correct.
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